Hence, the inductive construction of the polytope \(P_I\)  via a sequence of push-pull
polytopes repeats the inductive construction of the Bott–Samelson variety \(R_I\) .
On the other hand, the definition of \(P_I(\lambda )\)  by explicit inequalities together
with calculations in [1]} exhibit \(P_I(\lambda )\)  as the Karshon–Grossberg cube
for \(R_I\)  and \(\lambda \) .
